International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 11, Pages 783-788
doi:10.1155/S0161171200003057

Existence and uniqueness theorems for some fourth-order nonlinear boundary value problems

Ruyun Ma

Department of Mathematics, Northwest Normal University, Gansu, Lanzhou 730070, China

Abstract

Let G and f:[0,1]×ℝ4→ℝ be two functions satisfying Caratheodory conditions. This paper is concerned with the problems of existence and uniqueness of solutions for the nonlinear fourth-order ordinary differential equation y′′′′+λy′′+ky+G(x,y,y′,y′′,y′′′)=f(x,y,y′,y′′,y′′′) with one of a particular set of boundary conditions.